Leakage Inductance Determination for Transformers with Interleaving of Windings

Abstract

A diversity of formulas is given in literature for leakage inductance calculation of transformers with interleaving of windings. In the paper, the meaning of included terms and details of the application for concentric and pie windings transformers shall be discussed. Consid- ering the limitation of common formulas to magnetically symmetric transformers an alternative approach shall be demonstrated, which enables leakage inductance prediction also in the case of transformers with magnetically asymmetric arrangements of windings. 1. INTRODUCTION Several aspects of the operation of power-electronic circuits with transformers are signiflcantly in∞uenced by the leakage inductance of the respective transformer. For instance, it concerns power transfer capability of the circuit and power semiconductor stress parameters. The tendency to higher switching frequencies of power-electronic apparatuses results in an increasing relevance of low transformer leakage inductance values. Mostly, the so-called interleaving of windings (i.e., the fragmentation of the primary and the secondary windings into a certain number of sub-windings and alternate interleaving of primary and secondary sub-windings) is used to meet this requirement. Using an appropriate approximation method it is possible to determine the leakage inductance of a transformer already in the design phase on the basis of predicted geometry parameters. Thus, circuit simulation can be used to shorten the development process of power-electronic apparatuses. Formulas which are given in literature generally rely on an approximation method for leakage induc- tance determination which has been established by Rogowski (1). It is based on the consideration of the energy of the leakage magnetic fleld and applies to a transformer design with windings arranged on the same leg. The basic formula of this method is